The main objectives of the paper are to analyze the presence of Volatility in Indian Stock market and if present, to study the asymmetric nature and persistence behaviour of volatility in the Indian market using the Conditional Heteroscedasticity framework. Three models Of the Garch family (GARCH, E-GARCH and APARCH) are mainly focused for analytical purpose. The study has used NIFTY data and BSE data (April 1st 2004- April 1st 2014)as they capture more information compared to the bilateral daily exchange rate. From our readings it has been observed that the ARCH effect is significantly weak when compared to the Garch effect, which implies the weak reaction of conditional variance to shock. A high value of the GARCH coefficient indicates that volatility is present in the Indian Stock Market and is persistent in the long run. Further analysis reveals that the volatility is asymmetrical and the past negative shocks have a greater impact on the volatility than the past positive shocks.